Double bar graphs are an effective tool to compare the values of two quantities for the same observation. For example, consider the marks obtained by five students of a class in two tests. Using a double bar graph, we can analyse which week students had better marks.
Averages
Arithmetic Mean and Range
The average or arithmetic mean or mean of a given data is defined as :
Mean=Sum of all observations / Number of observations
The difference between the highest and the lowest observations in a given data is called its Range. Example: Ages of all 10 teachers in grade 7 are : 25, 43, 34, 55, 44, 60, 32, 29, 35, 40. Mean = 43+34+55+44+60,+32+29+35+40 = 39.7 years Range = Higest Observation – Lowest Observation = 60 – 25 = 35
Median
When a given data is arranged in ascending (or descending) order, then the middlemost observation is called the median of the data. Example : Marks scored by seven students in a class are: 21, 32, 18 ,93, 21, 36, 50. Observations in ascending order: 18, 21, 21, 32, 36, 50, 93. Middle most value = 32 ∴ Median is 32.
Mode
The mode of a set of observations is the observation that occurs most often. Example: Given set of numbers: 1, 1, 2, 4, 3, 2, 1, 2, 2, 4 Ascending Order = 1, 1, 1, 2, 2, 2, 2, 3, 4, 4 ∴ Mode of this data is 2 because it occurs more frequently. Note: A data can have more than 1 mode.
Chance and Probability
Probability is the measure or the chance of occurrence of a particular event. Experiments which do not have a fixed result are known as random experiments.
Number of outcomes or Sample Space The set of all the possible outcomes to occur in any experiment is known as sample space. Examples: Experiment : Tossing a coin, Sample Space (S) = {H,T}
Experiment : Rolling a die, Sample Space (S) = {1,2,3,4,5,6} Favourable outcome – It is one of the possible result(s) of an experiment. Examples : In an experiment of Tossing a coin, getting a head. Favourable outcome = {H} In an experiment of Rolling a die, getting an even number Favourable outcomes = {2,4,6} Probability of occurrence of any event,
P(E)=Number of favourable outcomes / Total Number of Outcomes
Example: Find the probability of getting an even number when a die is rolled. Sample Space (S) = {1,2,3,4,5,6} , Favourable outcomes = {2,4,6} P(E)=Number of favourable outcomes / Total Number of Outcomes =3/6=1/2
The Scale
Large numbers cannot be represented in a bar graph, so the scaling factor is used to reduce or scale down large numbers.
Organization of Data
Data is organised and represented graphically so that it becomes easy to understand and interpret. This is called an organisation of data.
Pictographs and Bar Graphs
A pictograph is a pictorial representation of data. Here data is represented using images of the objects.
Pictograph
The graphical representation of data using bars of uniform width drawn vertically or horizontally with different lengths is called as bar graphs/bar diagrams. Bar diagrams consist of two axes: X-axis and Y-axis. The following is a bar graph showing the birthday of students in a class. Graph showing the birthday of students in a class.
